Date -Day 0ET₀ 0 mm/dK_c 0ET_a 0 mm/dK_s 1Depletion 0 mmFPS 0

Drag to orbit, wheel or pinch to zoom. The cut face shows the root zone: blue = plant-available water, tan = depleted. White dots rising from the canopy are evapotranspiration; their number follows ET_a. The weather mast on the right measures what the Penman-Monteith equation needs.

Penman-Monteith Crop Water Lab

How much water does a maize field really use? Build a season from FAO-56 weather, crop coefficients and a root-zone bucket, then decide how to irrigate it.

Season

Maturity groupSoil

Irrigation strategy

Weather knobs

Live readouts

Daily evapotranspiration (mm/d)

Root-zone depletion (mm)

Experiments

Both run the whole season headless with the same weather, so the only difference is the thing being tested.

Independent numerical checks

Controls and missions

Drag / one finger: orbit; wheel / pinch: zoom. Climate presets restart the season. Sliders re-run the whole season with the same random seed, so you see the effect of one change at a time.
Mission 1: in the semi-arid preset, reach at least 95 % of potential yield with the least gross irrigation.
Mission 2: in the Mediterranean preset, find out how much yield one extra kelvin of warming costs with no irrigation.
Mission 3: in the monsoon preset, explain why most rain becomes deep percolation and irrigation is useless.
Mission 4: with fixed 7-day irrigation, change the soil to sandy loam and watch deep percolation.

The science

Reference evapotranspiration (FAO-56, eq. 6). ET₀ = [0.408 Δ (R_n − G) + γ 900/(T+273) u₂ (e_s − e_a)] / [Δ + γ (1 + 0.34 u₂)] in mm per day for a well-watered 0.12 m grass reference. Δ is the slope of the saturation vapour pressure curve, e_s(T) = 0.6108 exp(17.27 T/(T+237.3)), γ = 0.000665 P the psychrometric constant, and G is taken as 0 for daily steps. The first term is the radiation part and the second the aerodynamic (wind and dryness) part; the readouts show their split.

Radiation. Extraterrestrial radiation R_a comes from latitude, day of year and solar declination; solar radiation from sunshine fraction R_s = (0.25 + 0.50 n/N) R_a; net radiation R_n = 0.77 R_s − R_nl with the Stefan-Boltzmann outgoing term corrected for humidity and cloudiness.

Crop water use. ET_c = K_c ET₀ with the single crop coefficient rising from 0.30 to 1.20 through development, flat through mid-season and falling to 0.35 at maturity (typical FAO-56 maize values). Under stress ET_a = K_s K_c ET₀ with K_s = (TAW − D_r)/((1 − p) TAW) once the depletion D_r exceeds the readily available water RAW = p TAW; p is corrected for evaporative demand as in FAO-56 eq. 84.

Root-zone bucket. TAW = 1000 (θ_FC − θ_WP) Z_r with the root depth growing from 0.25 m to about 1 m. Daily: D_r,i = D_r,i−1 − (P − RO) − I + ET_a + DP; runoff RO uses the SCS curve number method; whatever would push the depletion below zero leaves as deep percolation DP. Newly reached soil is assumed to be at field capacity.

Yield. Relative yield follows the FAO-33 / Stewart linear relation 1 − Y_a/Y_m = K_y (1 − ET_a/ET_c) over the whole season with K_y = 1.25. Water productivity is Y_a/(10 ET_a) in kg per m³.

Simplifications and honesty. The weather is synthetic: a seeded generator produces daily rain (Markov wet-day chain with exponential depths), temperature, humidity, wind and sunshine around a hand-set climate; it mimics the character of each climate but is not a record of any place. Soil water constants, curve numbers, potential yields, and the irrigation efficiency of 85 % are typical or illustrative values, not measurements. A single K_c lumps soil evaporation and transpiration; there is no capillary rise, no salinity, no lateral flow and no separate stress timing (real crops are most sensitive around flowering). The yield formula is a first-order approximation. The 3D scene scales with growth stage but is not a crop growth model. Assets were modelled in Blender; the weather mast, growing plants and water particles are driven by the numbers on this page.